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Sharp spectral norm concentration and regularization of sparse random tensors

Year: 2026

Type: preprint

Abstract: We prove sharp spectral-norm bounds and construct a mean-fitting regularization procedure for sparse random tensors of fixed order $k$. For an $n\times\cdots\times n$ tensor with independentBernoulli$(p)$ entries, the centered norm is $O(\sqrt{np})$ with polynomially high probability whenever $np\ge c\log n$. This removes the logarithmic loss in Zhou and Zhu (2021). We also determine the expected centered norm at every sparsity level: for every $0

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.20520

Authors: Zhou, Zhixin, Zhu, Yizhe

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Simons Institute for the Theory of Computing, University of California Berkeley

OpenAlex ID: W7213604643

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